Figure REF  displays the voltage dependence of DL and FL torques, as well as the charge current density for several different values of the asymmetry parameter \(\delta \) . The horizontal dashed lines highlight the equilibrium values (at \(\mu _T = \mu _B\) ) of these quantities. As is apparent from the blue symbols in Fig. REF (a), the current-induced DL torque exerted on the free layer of a symmetric MTJ (\(\delta = 0\)  eV) switches sign as one reverses the voltage polarity, being more efficient when spin polarized electrons flow from the fixed to the free layer, i.e., at \(V>0\)  according to our convention. Such feature enables one to achieve bipolar-bidirectional magnetization switching whenever the torque intensity surpasses the intrinsic damping of a free layer [1]}, [2]}. The same qualitative features are also observed in asymmetric MTJs (\(\delta \ne 0\)  eV cases), but now with a smaller voltage modulation, i.e., smaller torque strength at a given voltage. It is worth emphasizing that the voltage modulation of the current density also drops with increasing \(\delta \)  such that the torque efficiency, defined as \(T_{DL}/J\) , might actually increase within some asymmetry window where the current density drops faster [3]}.
